An hp finite element method for a 4th order singularly perturbed boundary value problem in two dimensions. (1st October 2017)

• Record Type: Journal Article
• Authors: Constantinou, P.; Xenophontos, C.
• Is Part Of: Computers & mathematics with applications. Volume 74:issue 7(2017)
• Page Start: 1565
• Page End: 1575
• Publication Date: 2017-10-01
• Subjects: Fourth order singularly perturbed problem -- Boundary layers -- hp finite element method -- Robust exponential convergence; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.02.009
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We consider a fourth order singularly perturbed boundary value problem posed in a square and the approximation of its solution by the h p version of the finite element method on the so-called Spectral Boundary Layer mesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at an exponential rate when the error is measured in the energy norm. Our theoretical findings are illustrated through a numerical example.